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The ABC's of affine Grassmannians and Hall-Littlewood polynomials

We give a new description of the Pieri rule for k-Schur functions using the Bruhat order on the affine type-A Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and k-Schur functions.

preprint2016arXivOpen access
Avinash J. DalalJennifer Morse
math.COmath.AG
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Avinash J. DalalJennifer Morse

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